Intense Automorphisms of Finite Groups
2022
American Mathematical Society (Verlag)
978-1-4704-5003-8 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5003-8 (ISBN)
In this paper the authors classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges that the structure of such groups is almost completely determined by their nilpotency class: for p > 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group.
Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p?1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investigation that the structure of such groups is almost completely determined by their nilpotency class: for p > 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group.
Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p?1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investigation that the structure of such groups is almost completely determined by their nilpotency class: for p > 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group.
Mima Stanojkovski, Max Planck Institute, Leipzig, Germany.
| Erscheinungsdatum | 01.12.2021 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 241 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-5003-8 / 1470450038 |
| ISBN-13 | 978-1-4704-5003-8 / 9781470450038 |
| Zustand | Neuware |
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Buch | Softcover (2022)
Springer Spektrum (Verlag)
CHF 55,95
